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  • Master’s Thesis Financial Economics Erasmus School of Economics, Erasmus University Rotterdam

    Evaluating Multi-Horizon Volatility-Forecasting Performances of GARCH-Type Models

    Author: Han-Ywan Hu

    ERNA no.: 449758

    Supervisor: Dr Rogier Quaedvlieg

    Second assessor: Dr Esad Smajlbegovic

    Date: 7 February 2019

  • Acknowledgements

    I would like to express my sincere gratitude to Dr Rogier Quaedvlieg, my thesis supervisor, for his

    eternal patience, guidance, useful comments, and flexibility to let me pursue two banking internships

    at ABN AMRO and ING during my study. Besides, I would like to thank the second assessor for his

    courage to read this tedious paper. Furthermore, I would also like to thank my family, my dearest

    friends, and everyone else for their encouragement and support during this prolonged but rewarding

    journey. This accomplishment would have not been possible without them.

    万事开头难。

    冰冻三尺,非一日之寒。

    Rotterdam, 7 February 2019

    Han-Ywan Hu

    NON-PLAGIARISM STATEMENT By submitting this thesis the author declares to have written this thesis completely by himself/herself, and not to have used sources or resources other than the ones mentioned. All sources used, quotes and citations that were literally taken from publications, or that were in close accordance with the meaning of those publications, are indicated as such.

    COPYRIGHT STATEMENT The author has copyright of this thesis, but also acknowledges the intellectual copyright of contributions made by the thesis supervisor, which may include important research ideas and data. Author and thesis supervisor will have made clear agree- ments about issues such as confidentiality.

    Electronic versions of the thesis are in principle available for inclusion in any EUR thesis database and repository, such as the Master’s Thesis Repository of the Erasmus University Rotterdam

  • Evaluating Multi-Horizon Volatility-Forecasting Performances of GARCH-Type Models

    Han-Ywan Hu

    Erasmus School of Economics, Erasmus University Rotterdam

    7 February 2019

    Abstract

    This paper examines the forecast performances of several GARCH models at different horizons for

    equity indices from developed markets and emerging markets. It tries to find out which GARCH mod-

    els are best for short-term volatility forecasts and which ones perform best at longer horizons. Fur-

    thermore, we also study the underlying features that drive the forecast performance of GARCH mod-

    els at multiple horizons. We use the ARCH, GARCH, GJR-GARCH, CGARCH, APARCH, and GARCHX mod-

    els to forecast out-of-sample conditional variances of S&P 500, HSI, IPC, and KOSPI. The forecast per-

    formances are evaluated with MSE and QLIKE. Additionally, we test the significance of forecast losses

    with the Diebold-Mariano test and Model Confidence Set (MCS). The empirical findings of this paper

    are mixed, since there is not a single model that shows superior performance in each case. The

    GARCHX model, which incorporates the VIX, tends to generate superior forecasts at multiple horizons

    for the S&P 500, whereas in most cases CGARCH and APARCH are preferred under the remaining

    indices. Overall, we can conclude that conjoining a precise volatility proxy of an index to an ordinary

    GARCH model significantly improves the forecast performance, yet there are other factors as well that

    may influence the predictive ability of models.

    Keywords: Forecasting, ARCH, GARCH, GJR-GARCH, CGARCH, APARCH, GARCHX, Realised Volatility, VIX

    JEL: C22, C52, C53, C58

  • Table of contents

    §1. Introduction ...................................................................................................................................................... 1

    §2. Literature ........................................................................................................................................................... 3

    2.1. Multi-horizon forecasting................................................................................................................................................................ 3

    2.2. Empirical regularities of asset return volatility .................................................................................................................... 4

    • 2.2.1. Fat-tailed distributions .......................................................................................................................................................... 4

    • 2.2.2. Volatility clustering ................................................................................................................................................................. 4

    • 2.2.3. Long-memory property.......................................................................................................................................................... 4

    • 2.2.4. Leverage effect .......................................................................................................................................................................... 5

    • 2.2.5. Volatility-spillover effect ....................................................................................................................................................... 5

    • 2.2.6. Commonality in volatility changes .................................................................................................................................... 5

    §3. Methodology ..................................................................................................................................................... 6

    3.1. Volatility proxies ................................................................................................................................................................................. 6

    • 3.1.1. Squared return .......................................................................................................................................................................... 6

    • 3.1.2. Realised variance ..................................................................................................................................................................... 7

    • 3.1.3. Range-based variance ............................................................................................................................................................ 8

    3.2. Forecasting models ............................................................................................................................................................................ 9

    • 3.2.1. ARCH ............................................................................................................................................................................................. 9

    • 3.2.2. GARCH ....................................................................................................................................................................................... 10

    • 3.2.3. GJR-GARCH ............................................................................................................................................................................... 11

    • 3.2.4. CGARCH ..................................................................................................................................................................................... 11

    • 3.2.5. APARCH ..................................................................................................................................................................................... 12

    • 3.2.6. GARCHX ..................................................................................................................................................................................... 13

    3.3. Model fitting & forecast evaluation .......................................................................................................................................... 14

    • 3.3.1. Information criteria tests .................................................................................................................................................. 14

    • 3.3.2. Mean squared error ............................................................................................................................................................. 14

    • 3.3.3. Quasi-likelihood ..................................................................................................................................................................... 15

    • 3.3.4. Diebold-Mariano test ........................................................................................................................................................... 16

    • 3.3.5. Model Confidence Set ........................................................................................................................................................... 17

    3.4. Forecasting procedure ................................................................................................................................................................... 18

    §4. Data ....................................................................

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